Abstract

For the first time evidence is provided that one-dimensional objects formed by the accumulation of tracer particles can emerge in flows of thermogravitational nature (in the region of the space of parameters, in which the so-called OS (oscillatory solution)flow of the Busse balloon represents the dominant secondary mode of convection). Such structures appear as seemingly rigid filaments, rotating without changing their shape. The most interesting (heretofore unseen) feature of such a class of physical attractors is their variety. Indeed, distinct shapes are found for a fixed value of the Rayleigh number depending on parameters accounting for particle inertia and viscous drag. The fascinating “sea” of existing potential paths, their multiplicity and tortuosity are explained according to the granularity of the loci in the physical space where conditions for phase locking between the traveling thermofluid-dynamic disturbance and the “turnover time” of particles in the basic toroidal flow are satisfied. It is shown, in particular, how the observed wealth of geometric objects and related topological features can be linked to a general overarching attractor representing an intrinsic (particle-independent) property of the base velocity field.

Received 11 July 2012Accepted 07 December 2012Published online 09 January 2013

Lead Paragraph: Although three-dimensional (3D) time-dependent Rayleigh-Bénard (RB) convection has been the subject of a large amount of research, the associated problem related to the spontaneous accumulation (clustering) of solid particles dispersed in the fluid phase has not been similarly graced. Here this topic is investigated by direct numerical solution of the governing flow-field (Navier-Stokes-Boussinesq) equations in combination with a specific particle-tracking method accounting for particle motion under the influence of inertia and viscous drag. Attention is concentrated on a traveling-wave solution, which of RB convection represents a canonical state. It is shown that, if specific conditions are satisfied, particles, initially uniformly spaced in the liquid, are allowed to demix and form “apparently solid threads,” which rotate at an angular velocity equal to the angular frequency of the thermofluid-dynamic disturbance. The fascinating diversity and complexity of resulting shapes (changing according to inertial properties of particles) distinguish the present case from similar phenomena observed previously for Marangoni (thermocapillary) flow in systems with liquid/gas interfaces. The observed dynamics are explained in the framework of a theory that has its root in a long tradition of past studies devoted to phenomena of inertial particle clustering. This model does not require the presence of a free/liquid gas interface or other intrinsic features of Marangoni convection and is therefore applicable to a vast range of problems and situations.

Acknowledgments:

This work is supported by the Italian Space Agency (ASI) in the framework of the JEREMI (Japanese and European Research Experiment on Marangoni Instabilities) Project for the preparation and execution of an experiment onboard the International Space Station (ISS).